1. Construction will stop. Businessmen will not build if someone is going to tell them what rent they can expect.Read the rest at Gay Caswell's Blog.
2. Existing rental units will not be renovated and maintained. Businessmen cannot afford to run out and fix plumbing emergencies and paint rooms if their profit is gone.
3. Renters will be afraid to work or get better jobs because their rent will increase. They will be afraid to work themselves out of fixed rental brackets. That is bad for families and individuals. It encourages unemployment and living on welfare. People lose their sense of pride and responsibility.
4. More and more uncivil civil servants will be hired with an antagonism towards property owners and businessmen. More tax payer money will be wasted and more people will have to pay more taxes which will be used against them. There will be continued antagonism between renter and owner instead of mutual benefit.(...)
5. There will be a cry for more public housing because the private sector will not build if they cannot make a profit and if they cannot control their business.
6. Housing shortages will continue and grow worse.
7. Government waste and interference will grow worse.
8. Slums and families without homes to call their own will multiply.
If you want cheaper housing, build more of it and encourage home ownership. It's the law of supply and demand.